Math 74 (Topics in Topology) - Spring 2003

Text: Algebraic Topology by Alan Hatcher and Knots Knotes by Justin Roberts and Conway's ZIP Proof by J. Weeks and G. Francis

Knote: All the above materials are available on-line. If you want to purchase Hatcher's Book you can and the ZIP proof can also be found in Jeffrey R. Weeks' Shape of Space .

X-Session: The X-sessions will play a crucial role in this course. At each X-session we will meet and students will be randomly asked to describe their attempts at a solution to a selected homework problem. Grade: Your grade will be determined as follows: a midterm exam (30% of your grade), homework (30% of your grade), and a final exam (the remaining 40% of your grade).

Class Log: The homework assignments and exam due dates will be posted in the class log.

Honor Principle: On the exams, no help is to be given or received. On the homework, collaboration is permitted and encouraged.

Students with disabilities: I encourage students with disabilities, including "invisible" disabilities like chronic diseases and learning disabilities, to discuss with me any appropriate accommodations that might be helpful.

PRELIMINARY Syllabus: This class will cover several topics in combinatorial, algebraic and geometric topology. In particular, we will cover various topics in Knot Theory (see the Knots Knotes for details), we will classify surfaces (see the ZIP proof) and we will classify the covering spaces of a nice topological space (see chapter one of Hatcher). To accomplish these goals, we will need to carefully develop the notion of the fundamental group of topological space.